Apply 9: Cluster Model for S&P500
Paige Biester
2024-04-11
Set up
library(tidyverse)
library(tidyquant) # for financial analysis
library(broom) # for tidy model results
library(umap) # for dimension reduction
library(plotly) # for interactive visualizationData
# Get info on companies listed in S&P500
sp500_index_tbl <- tq_index("SP500")
# Get individual stocks from S&P500
sp500_symbols <- sp500_index_tbl %>% distinct(symbol) %>% pull()
# Get stock prices of the companies
sp500_prices_tbl <- tq_get(sp500_symbols, from = "2020-04-01")
write.csv(sp500_index_tbl, "../00_data/sp500_index_tbl.csv")
write.csv(sp500_prices_tbl, "../00_data/sp500_prices_tbl.csv")Import data
sp500_index_tbl <- read_csv("../00_data/sp500_index_tbl.csv")
sp500_prices_tbl <- read_csv("../00_data/sp500_prices_tbl.csv")
sp500_index_tbl %>% glimpse()## Rows: 504
## Columns: 9
## $ ...1 <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, …
## $ symbol <chr> "AAPL", "MSFT", "NVDA", "AMZN", "META", "BRK-B", "GOOGL…
## $ company <chr> "APPLE INC", "MICROSOFT CORP", "NVIDIA CORP", "AMAZON.C…
## $ identifier <chr> "037833100", "594918104", "67066G104", "023135106", "30…
## $ sedol <chr> "2046251", "2588173", "2379504", "2000019", "B7TL820", …
## $ weight <dbl> 0.063852496, 0.063282113, 0.058805166, 0.038154398, 0.0…
## $ sector <chr> "-", "-", "-", "-", "-", "-", "-", "-", "-", "-", "-", …
## $ shares_held <dbl> 185532921, 91814848, 302468387, 116491471, 27046746, 22…
## $ local_currency <chr> "USD", "USD", "USD", "USD", "USD", "USD", "USD", "USD",…sp500_prices_tbl %>% glimpse()## Rows: 629,218
## Columns: 9
## $ ...1 <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18…
## $ symbol <chr> "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL…
## $ date <date> 2020-04-01, 2020-04-02, 2020-04-03, 2020-04-06, 2020-04-07, …
## $ open <dbl> 61.6250, 60.0850, 60.7000, 62.7250, 67.7000, 65.6850, 67.1750…
## $ high <dbl> 62.1800, 61.2875, 61.4250, 65.7775, 67.9250, 66.8425, 67.5175…
## $ low <dbl> 59.7825, 59.2250, 59.7425, 62.3450, 64.7500, 65.3075, 66.1750…
## $ close <dbl> 60.2275, 61.2325, 60.3525, 65.6175, 64.8575, 66.5175, 66.9975…
## $ volume <dbl> 176218400, 165934000, 129880000, 201820400, 202887200, 168895…
## $ adjusted <dbl> 58.46381, 59.43937, 58.58514, 63.69596, 62.95821, 64.56961, 6…Question
Which stock prices behave similarly?
Our main objective is to identify stocks that exhibit similar price behaviors over time. By doing so, we aim to gain insights into the relationships between different companies, uncovering potential competitors and sector affiliations.
Why It Matters Understanding which companies are related is crucial for various reasons:
- Identifying Relationships: Clustering similar stocks reveals underlying connections and dependencies in the market.
- Competitor Analysis: Discovering competitors and sector affiliations aids in strategic planning and market positioning.
- Market Dynamics: Analyzing stock price similarities provides valuable insights into market dynamics, benefiting diverse fields such as finance, sales, and marketing.
Assignment Details Your task is to analyze the historical price data of various stocks and determine which stocks behave similarly. We will employ clustering techniques to accomplish this task effectively.
1 Convert data to standardized form
To compare data effectively, it must be standardized or normalized. Why? Because comparing values (like stock prices) of vastly different magnitudes is impractical. So, we’ll standardize by converting from adjusted stock price (in dollars) to daily returns (as percent change from the previous day). Here’s the formula:
\[ return_{daily} = \frac{price_{i}-price_{i-1}}{price_{i-1}} \]
sp500_prices_tbl %>% glimpse()## Rows: 629,218
## Columns: 9
## $ ...1 <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18…
## $ symbol <chr> "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL…
## $ date <date> 2020-04-01, 2020-04-02, 2020-04-03, 2020-04-06, 2020-04-07, …
## $ open <dbl> 61.6250, 60.0850, 60.7000, 62.7250, 67.7000, 65.6850, 67.1750…
## $ high <dbl> 62.1800, 61.2875, 61.4250, 65.7775, 67.9250, 66.8425, 67.5175…
## $ low <dbl> 59.7825, 59.2250, 59.7425, 62.3450, 64.7500, 65.3075, 66.1750…
## $ close <dbl> 60.2275, 61.2325, 60.3525, 65.6175, 64.8575, 66.5175, 66.9975…
## $ volume <dbl> 176218400, 165934000, 129880000, 201820400, 202887200, 168895…
## $ adjusted <dbl> 58.46381, 59.43937, 58.58514, 63.69596, 62.95821, 64.56961, 6…# Apply your data transformation skills!
sp_500_daily_returns_tbl <- sp500_prices_tbl %>%
select(symbol, date, adjusted) %>%
filter(date >= ymd("2018-01-01")) %>%
group_by(symbol) %>%
mutate(lag_1 = lag(adjusted)) %>%
ungroup() %>%
filter(!is.na(lag_1)) %>%
mutate(diff = adjusted - lag_1) %>%
mutate(pct_return = diff / lag_1) %>%
select(symbol, date, pct_return)
sp_500_daily_returns_tbl## # A tibble: 628,715 × 3
## symbol date pct_return
## <chr> <date> <dbl>
## 1 AAPL 2020-04-02 0.0167
## 2 AAPL 2020-04-03 -0.0144
## 3 AAPL 2020-04-06 0.0872
## 4 AAPL 2020-04-07 -0.0116
## 5 AAPL 2020-04-08 0.0256
## 6 AAPL 2020-04-09 0.00722
## 7 AAPL 2020-04-13 0.0196
## 8 AAPL 2020-04-14 0.0505
## 9 AAPL 2020-04-15 -0.00913
## 10 AAPL 2020-04-16 0.00795
## # ℹ 628,705 more rows2 Spread to object-characteristics format
We’ll convert the daily returns (percentage change from one day to the next) to object-characteristics format, also known as the user-item format. Users are identified by the symbol (company), and items are represented by the pct_return at each date.
stock_date_matrix_tbl <- sp_500_daily_returns_tbl %>%
spread(key = date, value = pct_return, fill = 0)
stock_date_matrix_tbl## # A tibble: 503 × 1,264
## symbol `2020-04-02` `2020-04-03` `2020-04-06` `2020-04-07` `2020-04-08`
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 A 0.0489 -0.0259 0.0560 -0.00444 0.0359
## 2 AAPL 0.0167 -0.0144 0.0872 -0.0116 0.0256
## 3 ABBV 0.0233 -0.0234 0.0322 -0.00449 0.0420
## 4 ABNB 0 0 0 0 0
## 5 ABT 0.0375 0.000126 0.0413 -0.00967 0.0369
## 6 ACGL 0.0115 -0.0650 0.0983 0.0314 0.0291
## 7 ACN 0.0103 -0.0264 0.0914 -0.0116 0.0464
## 8 ADBE 0.00913 -0.0341 0.0869 -0.0320 0.0267
## 9 ADI 0.0429 -0.0130 0.107 0.00470 0.0535
## 10 ADM 0.0136 0.00932 0.0326 0.00559 0.0139
## # ℹ 493 more rows
## # ℹ 1,258 more variables: `2020-04-09` <dbl>, `2020-04-13` <dbl>,
## # `2020-04-14` <dbl>, `2020-04-15` <dbl>, `2020-04-16` <dbl>,
## # `2020-04-17` <dbl>, `2020-04-20` <dbl>, `2020-04-21` <dbl>,
## # `2020-04-22` <dbl>, `2020-04-23` <dbl>, `2020-04-24` <dbl>,
## # `2020-04-27` <dbl>, `2020-04-28` <dbl>, `2020-04-29` <dbl>,
## # `2020-04-30` <dbl>, `2020-05-01` <dbl>, `2020-05-04` <dbl>, …3 Perform k-means cluster
stock_cluster <- kmeans(stock_date_matrix_tbl %>%
select(-symbol), centers = 5, nstart = 20)summary(stock_cluster)## Length Class Mode
## cluster 503 -none- numeric
## centers 6315 -none- numeric
## totss 1 -none- numeric
## withinss 5 -none- numeric
## tot.withinss 1 -none- numeric
## betweenss 1 -none- numeric
## size 5 -none- numeric
## iter 1 -none- numeric
## ifault 1 -none- numerictidy(stock_cluster)## # A tibble: 5 × 1,266
## `2020-04-02` `2020-04-03` `2020-04-06` `2020-04-07` `2020-04-08` `2020-04-09`
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.00620 -0.0196 0.0857 0.0129 0.0466 0.0273
## 2 0.0122 -0.0185 0.0913 -0.00447 0.0358 0.00646
## 3 0.0867 0.0170 0.0691 0.0345 0.0674 0.0143
## 4 -0.0167 -0.0262 0.114 0.0396 0.0627 0.0481
## 5 0.0226 -0.0113 0.0577 -0.00470 0.0350 0.0216
## # ℹ 1,260 more variables: `2020-04-13` <dbl>, `2020-04-14` <dbl>,
## # `2020-04-15` <dbl>, `2020-04-16` <dbl>, `2020-04-17` <dbl>,
## # `2020-04-20` <dbl>, `2020-04-21` <dbl>, `2020-04-22` <dbl>,
## # `2020-04-23` <dbl>, `2020-04-24` <dbl>, `2020-04-27` <dbl>,
## # `2020-04-28` <dbl>, `2020-04-29` <dbl>, `2020-04-30` <dbl>,
## # `2020-05-01` <dbl>, `2020-05-04` <dbl>, `2020-05-05` <dbl>,
## # `2020-05-06` <dbl>, `2020-05-07` <dbl>, `2020-05-08` <dbl>, …augment(stock_cluster, stock_date_matrix_tbl) %>%
ggplot(aes(symbol, `2020-04-02`, color = .cluster)) +
geom_point()
4 Select Optimal Number of Clusters
kclusts <- tibble(k = 1:9) %>%
mutate(kclust = map(.x = k, .f = ~ kmeans(stock_date_matrix_tbl %>%
select(-symbol), centers = .x, nstart = 20)),
glanced = map(.x = kclust, .f = glance))
kclusts %>%
unnest(glanced) %>%
ggplot(aes(k, tot.withinss)) +
geom_point() +
geom_line()
final_cluster <- kmeans(stock_date_matrix_tbl %>% select(-symbol), centers = 5, nstart = 20)5 Reduce Dimensions Using UMAP
umap_results <- stock_date_matrix_tbl %>%
select(-symbol) %>%
umap()
umap_results_tbl <- umap_results$layout %>%
as.tibble() %>%
bind_cols(stock_date_matrix_tbl %>% select(symbol))
umap_results_tbl## # A tibble: 503 × 3
## V1 V2 symbol
## <dbl> <dbl> <chr>
## 1 2.67 1.33 A
## 2 3.04 -0.543 AAPL
## 3 0.392 2.11 ABBV
## 4 2.41 -1.21 ABNB
## 5 1.30 1.72 ABT
## 6 -1.40 -0.706 ACGL
## 7 1.86 -0.0822 ACN
## 8 3.05 -0.473 ADBE
## 9 2.78 -2.20 ADI
## 10 -1.27 -0.436 ADM
## # ℹ 493 more rowsumap_results_tbl %>%
ggplot(aes(V1, V2)) +
geom_point()
6 Visualize Clusters by Adding k-means results
kmeans_umap_tbl <- final_cluster %>%
augment(stock_date_matrix_tbl) %>%
select(symbol, .cluster) %>%
left_join(umap_results_tbl) %>%
cross_join(sp_500_daily_returns_tbl %>%
select(-date) %>%
pivot_wider(names_from = symbol, values_from = pct_return) %>%
janitor::clean_names())
kmeans_umap_tbl## # A tibble: 503 × 507
## symbol .cluster V1 V2 aapl msft nvda amzn meta brk_b googl
## <chr> <fct> <dbl> <dbl> <list> <list> <list> <list> <list> <lis> <lis>
## 1 A 2 2.67 1.33 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 2 AAPL 5 3.04 -0.543 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 3 ABBV 1 0.392 2.11 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 4 ABNB 5 2.41 -1.21 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 5 ABT 1 1.30 1.72 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 6 ACGL 2 -1.40 -0.706 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 7 ACN 2 1.86 -0.0822 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 8 ADBE 5 3.05 -0.473 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 9 ADI 5 2.78 -2.20 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 10 ADM 2 -1.27 -0.436 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## # ℹ 493 more rows
## # ℹ 496 more variables: avgo <list>, goog <list>, tsla <list>, jpm <list>,
## # lly <list>, v <list>, unh <list>, xom <list>, cost <list>, ma <list>,
## # nflx <list>, wmt <list>, pg <list>, jnj <list>, hd <list>, abbv <list>,
## # ko <list>, crm <list>, bac <list>, pm <list>, cvx <list>, csco <list>,
## # mcd <list>, orcl <list>, abt <list>, ibm <list>, wfc <list>, lin <list>,
## # pep <list>, mrk <list>, ge <list>, t <list>, pltr <list>, vz <list>, …Help Please!
# g <- kmeans_umap_tbl %>%
# mutate(text_label = str_glue("Symbol: {symbol}
# Cluster: {.cluster}
#Date: {'2020-04-02' %>% scales::percent(1)}")) %>%
# ggplot(aes(V1, V2, color = .cluster, text = text_label)) +
# geom_point()
# g %>% ggplotly(tooltip = "text")